On the Existence of Projected Solutions of Quasi-Variational Inequalities and Generalized Nash Equilibrium Problems

Didier Aussel (), Asrifa Sultana and Vellaichamy Vetrivel
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Didier Aussel: Université de Perpignan Via Domitia
Asrifa Sultana: Indian Institute of Technology Madras
Vellaichamy Vetrivel: Indian Institute of Technology Madras

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 3, No 7, 818-837

Abstract: Abstract A quasi-variational inequality is a variational inequality, in which the constraint set is depending on the variable. However, as shown by a motivating example in electricity market, the constraint map may not be a self-map, and then, there is usually no solution. Thus, we define the concept of projected solution and, based on a fixed point theorem, we establish some results on existence of projected solution for quasi-variational inequality problem in a finite-dimensional space where the constraint map is not necessarily self-map. As an application of our results, we obtain an existence theorem for quasi-optimization problems. Finally, we introduce the concept of projected Nash equilibrium and study the existence of such equilibrium for noncooperative games as another application.

Keywords: Quasi-variational inequality; Generalized Nash equilibrium; Non-self map; 49J40; 90C26; 90B10 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10957-016-0951-9

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